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Abstract Population ecology and biogeography applications often necessitate the transfer of models across spatial and/or temporal dimensions to make predictions outside the bounds of the data used for model fitting. However, ecological data are often spatiotemporally unbalanced such that the spatial or the temporal dimension tends to contain more data than the other. This unbalance frequently leads model transfers to become substitutions, which are predictions to a different dimension than the predictive model was built on. Despite the prevalence of substitutions in ecology, studies validating their performance and their underlying assumptions are scarce.Here, we present a case study demonstrating both space‐for‐time and time‐for‐space substitutions (TFSS) using emperor penguins (Aptenodytes forsteri) as the focal species. Using an abundance‐based species distribution model (aSDM) of adult emperor penguins in attendance during spring across 50 colonies, we predict long‐term annual fluctuations in fledgling abundance and breeding success at a single colony, Pointe Géologie. Subsequently, we construct statistical models from time series of extended counts on Pointe Géologie to predict average colony abundance distribution across 50 colonies.Our analysis reveals that the distance to nearest open water (NOW) exhibits the strongest association with both temporal and spatial data. Space‐for‐time substitution performance of the aSDM, as measured by the Pearson correlation coefficient, was 0.63 and 0.56 when predicting breeding success and fledgling abundance time series, respectively. Linear regression of fledgling abundance on NOW yields similar TFSS performance when predicting the abundance distribution of emperor penguin colonies with a correlation coefficient of 0.58.We posit that such space–time equivalence arises because: (1) emperor penguin colonies conform to their existing fundamental niche; (2) there is not yet any environmental novelty when comparing the spatial versus temporal variation of distance to the nearest open water; and (3) models of more specific components of life histories, such as fledgling abundance, rather than total population abundance, are more transferable. Identifying these conditions empirically can enhance the qualitative validation of substitutions in cases where direct validation data are lacking. 

Abstract Many ecological systems dominated by stochastic dynamics can produce complex time series that inherently limit forecast accuracy. The ‘intrinsic predictability’ of these systems can be approximated by a time series complexity metric called weighted permutation entropy (WPE). While WPE is a useful metric to gauge forecast performance prior to model building, it is sensitive to noise and may be biased depending on the length of the time series. Here, we introduce a simple randomized permutation test (rWPE) to assess whether a time series is intrinsically more predictable than white noise.We apply rWPE to both simulated and empirical data to assess its performance and usefulness. To do this, we simulate population dynamics under various scenarios, including a linear trend, chaotic, periodic and equilibrium dynamics. We further test this approach with observed abundance time series for 932 species across four orders of animals from the Global Population Dynamics Database. Finally, using Adélie (Pygoscelis adeliae) and emperor penguin (Aptenodytes forsteri) time series as case studies, we demonstrate the application of rWPE to multiple populations for a single species.We show that rWPE can determine whether a system is significantly more predictable than white noise, even with time series as short as 10 years that show an apparent trend under biologically realistic stochasticity levels. Additionally, rWPE has statistical power close to 100% when time series are at least 30 time steps long and show chaotic or periodic dynamics. Power decreases to ~10% under equilibrium dynamics, irrespective of time series length. Among four classes of animal taxa, mammals have the highest relative frequency (28%) of time series that are both longer than 30 time steps and indistinguishable from white noise in terms of complexity, followed by insects (16%), birds (16%) and bony fishes (11%).rWPE is a straightforward and useful method widely applicable to any time series, including short ones. By informing forecasters of the inherent limitations to a system's predictability, it can guide a modeller's expectations for forecast performance. 

Like many polar animals, emperor penguin populations are challenging to monitor because of the species' life history and remoteness. Consequently, it has been difficult to establish its global status, a subject important to resolve as polar environments change. To advance our understanding of emperor penguins, we combined remote sensing, validation surveys and using Bayesian modelling, we estimated a comprehensive population trajectory over a recent 10-year period, encompassing the entirety of the species’ range. Reported as indices of abundance, our study indicates with 81% probability that there were fewer adult emperor penguins in 2018 than in 2009, with a posterior median decrease of 9.6% (95% credible interval (CI) −26.4% to +9.4%). The global population trend was −1.3% per year over this period (95% CI = −3.3% to +1.0%) and declines probably occurred in four of eight fast ice regions, irrespective of habitat conditions. Thus far, explanations have yet to be identified regarding trends, especially as we observed an apparent population uptick toward the end of time series. Our work potentially establishes a framework for monitoring other Antarctic coastal species detectable by satellite, while promoting a need for research to better understand factors driving biotic changes in the Southern Ocean ecosystem. 

Climate impacts are not always easily discerned in wild populations as detecting climate change signals in populations is challenged by stochastic noise associated with natural climate variability, variability in biotic and abiotic processes, and observation error in demographic rates. Detection of the impact of climate change on populations requires making a formal distinction between signals in the population associated with long-term climate trends from those generated by stochastic noise. The time of emergence (ToE) identifies when the signal of anthropogenic climate change can be quantitatively distinguished from natural climate variability. This concept has been applied extensively in the climate sciences, but has not been explored in the context of population dynamics. Here, we outline an approach to detecting climate-driven signals in populations based on an assessment of when climate change drives population dynamics beyond the envelope characteristic of stochastic variations in an unperturbed state. Specifically, we present a theoretical assessment of the time of emergence of climate-driven signals in population dynamics (urn:x-wiley:13541013:media:gcb16041:gcb16041-math-0001). We identify the dependence of urn:x-wiley:13541013:media:gcb16041:gcb16041-math-0002 on the magnitude of both trends and variability in climate and also explore the effect of intrinsic demographic controls on urn:x-wiley:13541013:media:gcb16041:gcb16041-math-0003. We demonstrate that different life histories (fast species vs. slow species), demographic processes (survival, reproduction), and the relationships between climate and demographic rates yield population dynamics that filter climate trends and variability differently. We illustrate empirically how to detect the point in time when anthropogenic signals in populations emerge from stochastic noise for a species threatened by climate change: the emperor penguin. Finally, we propose six testable hypotheses and a road map for future research. 

Abstract. The potential for multiyear prediction of impactful Earthsystem change remains relatively underexplored compared to shorter(subseasonal to seasonal) and longer (decadal) timescales. In this study, weintroduce a new initialized prediction system using the Community EarthSystem Model version 2 (CESM2) that is specifically designed to probepotential and actual prediction skill at lead times ranging from 1 month outto 2 years. The Seasonal-to-Multiyear Large Ensemble (SMYLE) consists of acollection of 2-year-long hindcast simulations, with four initializations peryear from 1970 to 2019 and an ensemble size of 20. A full suite of output isavailable for exploring near-term predictability of all Earth systemcomponents represented in CESM2. We show that SMYLE skill for ElNiño–Southern Oscillation is competitive with other prominent seasonalprediction systems, with correlations exceeding 0.5 beyond a lead time of 12months. A broad overview of prediction skill reveals varying degrees ofpotential for useful multiyear predictions of seasonal anomalies in theatmosphere, ocean, land, and sea ice. The SMYLE dataset, experimentaldesign, model, initial conditions, and associated analysis tools are allpublicly available, providing a foundation for research on multiyearprediction of environmental change by the wider community.